Remaining Loan Annuity
At a glance, the rest of a loan is easy to calculate if the remaining loan is previously known. But what if we want to calculate the remainder of a loan but the rest of the previous loan is unknown?
Information :
Sm = Remaining Loan at period m
Im = Residual interest at period m
i = percentage of interest per period
A loan of $10,000,000 will be repaid with a monthly annuity system with an interest rate of 3%/month for 2.5 years and the annuity is $510,192.59. Please specify the remaining loan after repayment for 10 months!
Answer :
i = 3%/month = 0.03/month
Determine first interest first:
$10,000,000 x 0.03 = $300,000
So the first interest is $ 300,000
Determine the first installment:
$510,192.59 - $300,000 = $210,192,59
Determine the 11th installment with the installment formula:
a11 = $210,192.59(1 + 0.03)11-1
a11 = $210,192.59(1,03)10
a11 = $210,192.59 x 1.3439164
a11 = $282,481.26
Determine the 11th interest:
I11 = $510,192.59 - $282,481.26
I11 = $227,711.33
So the rest of the loan after repayment for 10 months is 7,590,377.67.
Similarly this article.
Sorry if there is a wrong word.
The end of word wassalamualaikum wr. wb
Referensi :
Formula of Remaining Loan Annuity
Information :
Sm = Remaining Loan at period m
Im = Residual interest at period m
i = percentage of interest per period
Example Question of Remaining Loan Annuity
Answer :
i = 3%/month = 0.03/month
Determine first interest first:
$10,000,000 x 0.03 = $300,000
So the first interest is $ 300,000
Determine the first installment:
$510,192.59 - $300,000 = $210,192,59
Determine the 11th installment with the installment formula:
a11 = $210,192.59(1 + 0.03)11-1
a11 = $210,192.59(1,03)10
a11 = $210,192.59 x 1.3439164
a11 = $282,481.26
Determine the 11th interest:
I11 = $510,192.59 - $282,481.26
I11 = $227,711.33
So the rest of the loan after repayment for 10 months is 7,590,377.67.
Similarly this article.
Sorry if there is a wrong word.
The end of word wassalamualaikum wr. wb
Referensi :
- To'Ali's book math group accounting and sales
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